Finite rings with Eulerian zero-divisor graphs.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1260.16020
DOI: 10.1142/S0219498812500557
publication date: 2012-06-25T00:00:00Z
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 6049621
zbMATH Keywords: zero divisor graphs
zbMATH Keywords: Eulerian graphs
zbMATH Keywords: finite rings
author: A. S. Kuzmina
MaRDI profile type: Publication
cites work: When a zero-divisor graph is planar or a complete \(r\)-partite graph
cites work: On zero-divisor graphs of finite rings.
cites work: The zero-divisor graph of a commutative ring
cites work: Coloring of commutative rings
cites work: Planar zero-divisor graphs
cites work: Solvable and locally closed modules and rings
cites work: Q5622399
cites work: NILPOTENT FINITE RINGS WITH PLANAR ZERO-DIVISOR GRAPHS
cites work: Zero square rings
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published in: Journal of Algebra and its Applications
title: Finite rings with Eulerian zero-divisor graphs.
review text: The author describes all finite associative (not necessarily commutative) rings whose zero divisor graphs are Eulerian. A zero divisor graph \(\Gamma(R)\) in this paper has the vertex set consisting of all one-sided and two sided zero divisors, and two distinct vertices \(x\) and \(y\) are adjacent if and only if either \(xy=0\) or \(yx=0\).
reviewed by: Tongsuo Wu
description: scientific article; zbMATH DE number 6049621